子供の為に is a purpose with the verb left off, as in the English. 子供 kodomo is a child or the children, one or many. の為に no tame ni is for the sake of, with the older sense of benefit behind it. What one does for them is left to the reader. Japanese drops the possessor, so the line holds my children and our children at once.
The phrase has no author; in the medieval war tales it is a mother's reason with her sons' lives at stake, said by the Soga brothers' mother in the Soga monogatari (in print by 1627) and given to her again by Chikamatsu in 1718, and in English it is the title of Dennis Ogawa's 1978 history of the Japanese in Hawaii.
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